Environmental Engineering Reference
In-Depth Information
energy assessment analyses and wind load studies. Therefore, the following analysis will use
the Weibull distribution, although the same general procedures would apply to other math-
ematical models.
Weibull Wind Speed Distribution Functions
In Equation (8-4b)
F
is the
cumulative distribution function
which defines the so-called
wind duration curve.
The Weibull equation for the duration curve is
F
(
U
1
³
U
) = 8,760 exp [- (
U
/
C
)
k
]
(8-5)
where
exp[ ] = exponential function of [ ]
C =
empirical Weibull scale factor (m/s)
k
=
empirical Weibull shape factor
Duration curves for several values of the shape factor
k
are shown in Figure 8-6. The range
from 1.5 to 3.0 for
k
includes most site wind conditions. The
Rayleigh distribution
is a
special case of the Weibull distribution in which the shape factor is 2.0. Cliff [1977]
suggests that sites with annual average wind speeds greater than 4.5 m/s tend to have a
near-Rayleigh cumulative wind distribution.
Substituting Equation (8-5) into (8-4b), the Weibull frequency distribution function is
f
U
= (8,760/
C
)
k
(
U
/
C
)
k
-
1
exp [- (
U
/
C
)
k
]
(8-6)
from which we can calculate the annual average wind speed to be
U
a
=
C
G(1+ 1/
k
) » (0.90 ± 0.01)
C
(8-7)
where
U
a
=
annual average wind speed (m/s)
G( ) = gamma function of ( )
Figure 8-7 shows the Weibull frequency distribution curves associated with the duration
curves in Figure 8-6 and the annual average wind speed for each value of
k.
Note that the
annual average wind speed is higher than the most-frequent wind speed, but that these two
parameters approach equality at higher values of
k.
Reference Wind Speed Distribution
Early in the U.S. Federal Wind Energy Program a reference annual wind speed distri-
bution was defined to serve as a uniform basis for research and development projects. To
be representative of a large portion of the worldwide wind resource, the annual average
wind speed was selected to be 6.26 m/s (14 mph) at an elevation of 9.1 m (30 ft) above
level terrain. Weibull factors for this reference distribution are
C
= 7.17 m/s and
k
= 2.29.
The resulting duration and frequency curves are shown in Figures 8-6 and 8-7. Additional
details on the reference wind speed distribution are given in Chapter 2.
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